Already known is a three-way catalytic converter, by which three major toxic components (HC, CO and NO.sub.x) in the gas exhausted from an internal combustion engine can be eliminated. The operation of this known three-way catalytic converter is effectively attained when an atmosphere of the exhaust gas introduced into the converter is controlled near stoichiometric atmosphere in which excess air or excess fuel is not substantially left in the exhaust gas, i.e., wherein the excess air ratio .lambda. of the exhaust gas is kept near 1.0.
However, it is impossible to keep the .lambda. near 1.0 in the known carburetor type internal combustion engine; therefore, an effective operation of the three-way catalytic converter is not expected.
Therefore, various types of apparatus have been heretofore proposed for introducing an amount of secondary air into the exhaust pipe of the engine from an air source (for example, an air pump). In these known apparatus, the amount of air introduced into the exhaust pipe is controlled, by a single air flow control valve operated by electric signals from a .lambda. sensor arranged in the exhaust pipe, in such a manner that the amount of air is increased when .lambda. &lt; 1.0 (in other words, when an excess of fuel remains in the exhaust gas), and the amount of air is decreased when .lambda. &gt; 1.0 (in other words, when an excess of air remains in the exhaust gas). As a result of this, controlling the atmosphere of the exhaust gas to the stoichiometric atmosphere (in which .lambda. = 1.0) can be expected.
However, in these known apparatus, a precise control of the atmosphere cannot be fully expected. This is because, the amount of air introduced into the valve from the air pump, which is directly connected to the air flow control valve, is independent of the amount of secondary air which should be introduced into the exhaust pipe from the valve. Because there is no relation between the amount of air which is introduced into the air flow control valve and the amount of air which is discharged from the valve, an effective atmospheric control operation cannot be expected to be performed by the valve.